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  4. If p and q are order and degree of differential equation y2((d2 y/d x2))2+3 x((d y/d x))1 / 3+x2 y2= sin x, then :

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Q. If $p$ and $q$ are order and degree of differential equation $y^2\left(\frac{d^2 y}{d x^2}\right)^2+3 x\left(\frac{d y}{d x}\right)^{1 / 3}+x^2 y^2=\sin x$, then :

Differential Equations

Solution:

$y^2\left(\frac{d^2 y}{d x^2}\right)^2+x^2 y^2-\sin x=-3 x\left(\frac{d y}{d x}\right)^{1 / 3}$
$\left(y^2\left(\frac{d^2 y}{d x^2}\right)^2+x^2 y^2-\sin x\right)^3=-27 x^3\left(\frac{d y}{d x}\right)$
here order $=2=p$
Degree $=6=q$
$\therefore p < q$